Chapter 4.4, Problem 64E

True or false? In Exercises $63$and $64$, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.

$\left(\text{a}\right)$ A set $S=\left\{v_{\text{1}}\text{,}{v}_{\text{2}}\text{,}\mathrm{...}\text{,}{v}_{\text{k}}\right\}$, $k\ge 2$ is linearly independent if and only if at least one of the vectors $v_i$ can be written as linear combination of the other vectors in $S$.

$\left(\text{b}\right)$ If a subset $S$ spans a vector space $V$, then every vector in $V$ can be written as a linear combination of the vectors in $S$.